The positive test has thrown their tournament preparations into chaos with the team forced to pull out of Tuesday's warm-up friendly against Lithuania.
The Spanish football federation said in a statement on the national team's website that 32-year-old Barcelona midfielder Busquets had tested positive on Sunday and had left the camp.
The rest of the squad had tested negative but Busquets and his contacts would remain isolated.
Spain's friendly against Lithuania will now be played by their under-21 squad, the statement said, with the federation offering refunds to those who had bought tickets and did not want to go and discounts to those who still wanted to attend.
Spain begin their Euro 2020 campaign against Sweden in Seville on June 14 before playing Group E fixtures against Poland on June 19 and Slovakia four days later.
